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What is the TMUA?

The TMUA is a maths admissions test introduced in 2016. It consists of two multiple choice papers sat at the end of October. Although the test is not compulsory anywhere, universities such as Durham, Warwick and Lancaster will set an easier offer based on a good TMUA score.

The two papers are:

  • Paper 1: Mathematical Thinking, made up of 20 multiple choice questions 
  • Paper 2: Mathematical Reasoning, made up of 20 multiple choice questions

Each paper lasts 1 hour and 15 minutes. As all of the TMUA is multiple choice, any preparation you do for the MAT multiple choice will be incredibly useful here. It is sat at the end of October, about the same time as the MAT. You can, however, do both – as I did. 

What do you need to revise?

The TMUA has the same syllabus as the MAT. You are expected to have a good grasp of first-year A-Level Pure Maths, as well as sequences and series. There is also an emphasis on your mental arithmetic skills and numerical skills. This includes the ability to: 

  • Convert between fractions and percentages
  • Use surds and π in exact collections (as in, not approximating them, but being able to leave them as a symbol in final answers.) 
  • Approximate and use approximation to find upper and lower bounds. 

This is important because both TMUA papers, like the MAT, are non-calculator. There is also no formula book, so make sure you memorise all the formulas you have come across in your first year of Pure Maths. 

Paper 1 focuses on your ability to apply your knowledge of maths in foreign situations. That is, the questions will apply your knowledge from A-Level Mathematics. They want to see you can apply it, not just memorise it. 

For example, you may get questions about:

  • Differentiating functions with lots of terms. For example, the logarithm and exponential function
  • Rearranging complex formulae
  • Wordy probability problems, where the formula you need to know is not immediately clear
  • Finding regions of trigonometric functions where certain conditions are satisfied 
  • Integration of two shapes overlapping on the Cartesian plane
  • Finding terms of a sequence
  • Using the trapezium rule, especially to work out when it gives an overestimate or an underestimate
  • Solving non-linear simultaneous equations

Essentially, the Paper 1 questions will be like a selection of the hardest questions that appear in your A-Level Maths

What about Paper 2?

Paper 2 assesses your skills at justifying and interpreting mathematical arguments and conjectures, and your ability to deal with basic concepts from logic. This is very different to the style of A-Level questions, whereas Paper 1 mirrors them.

It is definitely worth doing more preparation and practice for this section. You will have some questions about functions, differentiation, and sequences, which are similar to those you answer at the harder end of A-Level. But there will also be some questions of a very different style, such as: 

  • You are presented with a step-by-step proof of a theorem and have to work out where the proof went wrong
  • You are asked to comment on a proof, from a given number of options; for example, saying it is incorrect, incomplete, or where it went wrong. 
  • You are given a statement and have to deduce from a list of options which one of them is a sufficient condition for this statement to hold. 
  • Choosing correct statements based on a graph you are presented with. 
  • Manipulating numbers in standard form, and doing algebra on them. 
  • You are asked to translate a graph given only as a picture, without an equation, and you must see which of the options provided could be the new translated graph. 
  • Selecting from a list which one is a counterexample to a proposition. 
  • Being given statements about prime numbers, square numbers or cube numbers, and having to work out which statement holds universally. 

The style of some of the questions in Paper 2 is very different to those approached at A-Level, with the purpose of exposing you to more mathematical logic, something central to maths at university. 

Which universities consider the TMUA?

You are encouraged to sit the TMUA if you are applying to study Maths or Maths joint honour courses at: 

  • Durham University
  • Lancaster University
  • University of Warwick
  • University of Sheffield
  • University of Southampton
  • London School of Economics and Political Science (LSE)

The test is not compulsory for any of these universities. But performing well in the TMUA can lead to a reduced offer, giving you extra security while you await your results in August. 


Taking the TMUA is definitely worthwhile if you’re applying to one of the universities above. To find out how you can best prepare for the TMUA, see our Ultimate TMUA Preparation Guide.